MIAMI BEACH — If he is convicted of all the crimes linked to him, high-profile fugitive Andrew Cunanan could achieve a distinctive place among the gruesome pantheon of serial killers.

Even the experts were shocked by the brazenness of the public killing last week of world-famous fashion designer Gianni Versace, for which Cunanan is the prime suspect.

FOR THE RECORD - Additional material published July 29, 1997:Corrections and clarifications.In the July 20 coverage of fugitive Andrew Cunanan, it was erroneously reported that Cunanan had fathered a pre-school-age daughter. The information, provided by a federal fugitive task force hunting Cunanan, was later amended to identify him not as the girl's father but as her godfather. The Tribune regrets the error.

"There aren't many serial killers who have killed famous people," said James Allen Fox, dean of the College of Criminal Justice at Northeastern University in Boston. "Mostly, they select obscure victims who are accessible."

Cunanan's cross-country flight is a study in contrasts, beginning with four alleged murders painstakingly hidden to allow the attacker ample time to flee. Then came the slaying of Versace, a crime that appeared to be a polar opposite of the others.

The seemingly erratic pattern of Cunanan's alleged crimes clearly complicates the task of his pursuers. Even so, experts say there is no such thing as a textbook serial killer.

"They've all got their idiosyncrasies," explained retired FBI agent Bill Hagerty, who was involved in the investigation of serial killer Ted Bundy.

"They're pushed by whatever fantasy they have that turns them on. To some it may be the sexual act, to others it's the pursuit, and to others it's the taunting of authority."

Versace's death has launched a cottage industry in analyzing the mind and motives of Cunanan, his alleged assailant. Criminologists and psychologists have argued semantic points over what genus of fiend an alleged criminal like Cunanan might properly be assigned to--spree killer, serial killer or nomadic killer.

And they're arguing about what may be driving him.

One theory--unproven, of course, like all the others--is that Cunanan had recently learned he was HIV positive and was seeking revenge on former lovers.

The San Diego Union-Tribune reported Saturday that Cunanan had told a self-described counselor that he might have contracted the AIDS virus and would "get" the person who may have transmitted it to him.

Police have been unable to verify whether Cunanan does indeed carry the virus that causes AIDS. And while he knew two of the victims, the others may have been strangers.

Another theory is that Cunanan may have snapped because his high-flying lifestyle had unraveled: He was broke, had lost a wealthy suitor who had supported him for years and been rejected by another man he loved, Jeffrey Trail, who allegedly became Cunanan's first victim.

Still another theory is that Trail tried to interfere with Cunanan's efforts to rekindle a romance with David Madson, a Minneapolis architect, who was the second in the string to die.

Such conjecture might explain the early deaths, but the speculation gets fuzzier as the body count rises. Cunanan allegedly stole getaway cars from Chicago developer Lee Miglin, the third victim, and William Reese, a New Jersey cemetery caretaker who was next.

But Miglin's slaying in his Gold Coast home was so vicious that it raises questions about whether it was merely an act of convenience to obtain a vehicle and stay ahead of police.

Miglin's face was carefully wrapped in masking tape with a hole around the nostrils, and his chest was crushed and riddled with puncture wounds, apparently from a screwdriver.

The attack on Versace also defies easy explanation. The killing--in daylight and in public-- was risky and would only complicate efforts to avoid capture.

Afterward, though, Cunanan's notoriety was greater than ever, and the crime spree was international news.

And that could have been the point. "It would seem he's enjoying the chase and knowing police are looking for him," Hagerty theorized.

If true, Cunanan may be following a trail blazed by many serial killers, from Bundy, who bragged after being caught that he viewed killing as a test of his skills, to "Son of Sam" David Berkowitz, who teased his murders in letters to newspapers.

Given that so much is yet unknown about Cunanan's possible motives, it shouldn't be surprising that for every theory about Cunanan there is a counter-theory.

Robert Scigalski, a former FBI official in Chicago, sees Cunanan not as someone enjoying a deadly game but as a man who is losing control.

"No longer is he the gregarious, look-at-me charmer and center of attention who loves to talk to people and be `in your face' about himself," said Scigalski, who headed the bureau's behavioral profiling and fugitive apprehension units in Chicago before joining Schaumburg-based Quest Consultants International. "Now, he can't show himself, which seems to be a basic part of his personality, for fear of arrest. So he is not the personality he used to be, and that is disturbing. I see a degeneration."

Targeting someone of Versace's stature might be unusual for a serial killer, but in other ways the criminal activities attributed to Cunanan fit some familiar patterns.